Instabilities of fully developed rapid flow of a granular material in a channel

1997 ◽  
Vol 342 ◽  
pp. 179-197 ◽  
Author(s):  
CHI-HWA WANG ◽  
R. JACKSON ◽  
S. SUNDARESAN
Keyword(s):  
Granular Material ◽  
Particle Concentration ◽  
Travelling Waves ◽  
Equations Of Motion ◽  
Axial Direction ◽  
Small Perturbations ◽  
Rapid Flow ◽  
The Mean ◽  
The Stability ◽  
Mean Concentration

The equations of motion for ‘rapid’ flow of a granular material have fully developed solutions representing flow driven by a body force, such as gravity, along a channel bounded by plane parallel walls. The stability of these solutions to small perturbations is investigated. For given properties of the particles and the channel walls it is found that the condition of critical stability is a relation between the mean concentration of the particles and the width of the channel. When the base state is unstable the fastest growing modes are travelling waves propagating in the axial direction and these induce characteristic patterns of variations in particle concentration, as well as velocity. These instabilities are contrasted with those found for Couette shearing in an earlier publication.

Instant 99mTc-Labelled Glucoheptonate Kit for Kidney Imaging

1983 ◽  
Vol 22 (05) ◽  
pp. 246-250 ◽  
Author(s):  
M. Al-Hilli ◽  
H. M. A. Karim ◽  
M. H. S. Al-Hissoni ◽  
M. N. Jassim ◽  
N. H. Agha
Keyword(s):  
Sodium Hydroxide Solution ◽  
Normal Subjects ◽  
Organ Distribution ◽  
Stable Complex ◽  
Scintillation Camera ◽  
Ph Adjustment ◽  
The Mean ◽  
The Stability ◽  
Kidney Imaging ◽  
Mean Concentration

Gelchromatography column scanning has been used to study the fractions of reduced hydrolyzed 99mTc, 99mTc-pertechnetate and 99mTc-chelate in a 99mTc-glucoheptonate (GH) preparation. A stable high labelling yield of 99mTc-GH complex in the radiopharmaceutical has been obtained with a concentration of 40-50 mg of glucoheptonic acid-calcium salt and not less than 0.45 mg of SnCl2 2 H2O at an optimal pH between 6.5 and 7.0. The stability of the complex has been found significantly affected when sodium hydroxide solution was used for the pH adjustment. However, an alternative procedure for final pH adjustment of the preparation has been investigated providing a stable complex for the usual period of time prior to the injection. The organ distribution and the blood clearance data of 99mTc-GH in rabbits were relatively similar to those reported earlier. The mean concentration of the radiopharmaceutical in both kidneys has been studied in normal subjects for one hour with a scintillation camera and the results were satisfactory.

scholarly journals On the Stability of Collinear Points of the RTBP with Triaxial and Oblate Primaries and Relativistic Effects

2021 ◽  
pp. 56-73
Author(s):  
S. E. Abd El-Bar
Keyword(s):  
Characteristic Equation ◽  
Body Problem ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Relativistic Effects ◽  
Three Body Problem ◽  
Total Potential ◽  
The Mean ◽  
The Stability ◽  
Three Body

Under the influence of some different perturbations, we study the stability of collinear equilibrium points of the Restricted Three Body Problem. More precisely, the perturbations due to the triaxiality of the bigger primary and the oblateness of the smaller primary, in addition to the relativistic effects, are considered. Moreover, the total potential and the mean motion of the problem are obtained. The equations of motion are derived and linearized around the collinear points. For studying the stability of these points, the characteristic equation and its partial derivatives are derived. Two real and two imaginary roots of the characteristic equation are deduced from the plotted figures throughout the manuscript. In addition, the instability of the collinear points is stressed. Finally, we compute some selected roots corresponding to the eigenvalues which are based on some selected values of the perturbing parameters in the Tables 1, 2.

Stability of Bortezomib 1-mg/mL Solution in Plastic Syringe and Glass Vial

2005 ◽  
Vol 39 (9) ◽  
pp. 1462-1466 ◽  
Author(s):  
Pascal André ◽  
Salvatore Cisternino ◽  
Fouad Chiadmi ◽  
Audrey Toledano ◽  
Joël Schlatter ◽  
...  
Keyword(s):  
Storage Temperature ◽  
Color Change ◽  
Hplc Method ◽  
Initial Concentration ◽  
Plastic Syringe ◽  
The Mean ◽  
The Stability ◽  
And Storage ◽  
Mean Concentration ◽  
Antineoplastic Chemotherapy

BACKGROUND: The proteasome inhibitor bortezomib (BTZ), used in antineoplastic chemotherapy, must be diluted in NaCl 0.9% for injection and stored for no more than 3 hours in a syringe or 8 hours in a vial. Better information on its stability could improve storage. OBJECTIVE: To assess the stability of BTZ solution (1 mg/mL) in syringes and vials. METHODS: BTZ 1-mg/mL solutions were prepared by adding sterile NaCl 0.9% to Velcade vials containing 3.5 mg of lyophilized BTZ. Syringes were filled with 1 mL of solution and stored in the dark at 5 °C or 60 °C; others were not protected from light and stored at 22 °C. Velcade vials containing 1 mL of solution were stored at 5 °C in the dark. Samples were taken at various times over 23 days and assayed in duplicate. An HPLC method for assaying the stability of BTZ was validated. Appearance and pH were recorded. RESULTS: There was no color change or precipitation in the samples, and the pH was stable. Oxidation, light, and storage temperature all affected the chemical stability of BTZ. The mean concentrations of BTZ in syringes stored for 2, 3, and 5 days at 60, 22, and 5 °C were >95% of the initial concentration. The mean concentration of BTZ in vials stored for 5 days at 5 °C was >95% of the initial concentration. CONCLUSIONS: BTZ stored refrigerated in vials or syringes and protected from light is chemically stable for 5 days after reconstitution.

Stability of Sotalol in Two Liquid Formulations at Two Temperatures

2003 ◽  
Vol 37 (4) ◽  
pp. 506-509 ◽  
Author(s):  
Milap C Nahata ◽  
Richard S Morosco
Keyword(s):  
Dosage Form ◽  
Physical Stability ◽  
Initial Concentration ◽  
Three Samples ◽  
Life Threatening ◽  
Two Temperatures ◽  
The Mean ◽  
The Stability ◽  
Liquid Dosage Form ◽  
Mean Concentration

BACKGROUND: Sotalol is used in certain pediatric patients to treat, suppress, or prevent the recurrence of life-threatening ventricular arrhythmias. However, it is commercially unavailable in a liquid dosage form. The use of an extemporaneously prepared liquid dosage form must be supported by the documentation of the chemical and physical stability of sotalol. OBJECTIVE: To determine the stability of sotalol hydrochloride extemporaneously prepared from tablets in 2 oral suspensions stored at 2 temperatures. METHODS: Five bottles contained Ora Plus: Ora Sweet (1:1) and the other 5 bottles had 1% methylcellulose:simple syrup NF (1:9), with a sotalol concentration of 5 mg/mL. Three samples were collected from each bottle at 0, 7, 14, 28, 42, 56, 70, and 91 days and analyzed by a stability-indicating HPLC analytical method (n = 15). RESULTS: At 4°C, the mean concentration of sotalol was at least 98.9% of the original concentration in Ora Plus: Ora Sweet suspension and 95.5% of the initial concentration in 1% methylcellulose:simple syrup during storage for 3 months. At 25°C, the mean concentration of sotalol was ≥95.5% of the original concentration in Ora Plus: Ora Sweet suspension and 94.4% of the initial concentration in 1% methylcellulose:simple syrup during storage for 3 months. The pH did not change substantially during the study period. Further, no changes in physical appearance were seen during the study. CONCLUSIONS: Sotalol hydrochloride can be prepared in either of 2 liquid dosage forms and stored in plastic bottles for 13 weeks at 4 or 25°C without substantial loss of potency.

Dynamic Stability of a Spinning Timoshenko Beam Subjected to a Moving Mass-Spring-Damper Unit

2010 ◽  
Author(s):  
T. H. Young ◽  
M. S. Chen
Keyword(s):  
Dynamic Stability ◽  
Timoshenko Beam ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Axial Direction ◽  
Longitudinal Axis ◽  
Moving Mass ◽  
The Stability ◽  
The Galerkin Method ◽  
Mass Spring

This paper investigates the dynamic stability of a finite Timoshenko beam spinning along its longitudinal axis and subjected to a moving mass-spring-damper (MSD) unit traveling in the axial direction. The mass of the moving MSD unit makes contact with the beam all the time during traveling. Due to the moving MSD unit, the beam is acted upon by a periodic, parametric excitation. In this work, the equations of motion of the beam are first discretized by the Galerkin method. The discretized equations of motion are then partially uncoupled by the modal analysis procedure suitable for gyroscopic systems. Finally the method of multiple scales is used to obtain the stability boundaries of the beam. Numerical results show that if the displacement of the MSD unit is equal to only one of the two transverse displacements of the beam, very large unstable regions may appear at main resonances.

Instability and filamentation of finite-amplitude waves on vortex layers of finite thickness

1989 ◽  
Vol 209 ◽  
pp. 359-384 ◽  
Author(s):  
D. I. Pullin ◽  
P. A. Jacobs ◽  
R. H. J. Grimshaw ◽  
P. G. Saffman
Keyword(s):  
Equations Of Motion ◽  
Finite Thickness ◽  
Finite Amplitude ◽  
Amplitude Wave ◽  
Small Perturbations ◽  
Interface Evolution ◽  
Weakly Nonlinear ◽  
The Mean ◽  
Finite Amplitude Waves ◽  
Nonlinear Interface

We study the instability of finite-amplitude waves on uniform vortex layers of finite thickness bounded by a plane rigid surface. A weakly nonlinear analysis of vorticity interface perturbations, and spectral stability calculations using the full equations of motion, together show that steady progressive waves are unstable to general subharmonic pertubations in the range 0.094 < d/λ < 1.7, where d is the mean layer thickness and λ is the primary wavelength. The relevance of this instability to ultimate interface filamentation is tested by performing several numerical contourdynamical simulations of the nonlinear interface evolution for initial disturbances consisting of the finite amplitude wave plus eigenfunctions obtained from the spectral calculations. The results indicate that within the band of unstable wavelengths, small perturbations to the steady non-uniform flow given by the finite amplitude wave motion (vortex equilibrium) are able to grow in magnitude, until at a time tf, the wave extremum encounters a hyperbolic critical point of the velocity field after which filamentation occurs. Arguments are put forward based on the unsteady simulations with the purpose of identifying the preferred frame of reference for viewing the kinematical events controlling the filamentation process. An estimate for tf is then made, and the mechanism of filamentation found is discussed in relation to the recently proposed nonlinear-cascade mechanism of Dritschel (1988a).

Nonlinear Planar Dynamics of Fluid-Conveying Cantilevered Extensible Pipes

2013 ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Michael P. Païdoussis ◽  
Marco Amabili
Keyword(s):  
Flow Velocity ◽  
Trivial Solution ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Time Integration ◽  
Axial Direction ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Critical Flow Velocity ◽  
The Stability

This paper for the first time investigates the nonlinear planar dynamics of a cantilevered extensible pipe conveying fluid; the centreline of the pipe is considered to be extensible resulting in coupled longitudinal and transverse equations of motion; specifically, the kinetic and potential energies are obtained in terms of longitudinal and transverse displacements and then the extended version of the Lagrange equations for systems containing non-material volumes is employed to derive the equations of motion. Direct time integration along with the pseudo-arclength continuation method are employed to solve the discretized equations of motion. Bifurcation diagrams of the system are constructed as the flow velocity is increased as the bifurcation parameter. As opposed to the case of an inextensible pipe, an extensible pipe elongates in the axial direction as the flow velocity is increased from zero. At the critical flow velocity, the stability of the system is lost via a supercritical Hopf bifurcation, emerging from the trivial solution for the transverse displacement and non-trivial solution for the longitudinal displacement and leading to a flutter.

Stability of Spironolactone in an Extemporaneously Prepared Suspension at Two Temperatures

1993 ◽  
Vol 27 (10) ◽  
pp. 1198-1199 ◽  
Author(s):  
Milap C. Nahata ◽  
Richard S. Morosco ◽  
Thomas F. Hippie
Keyword(s):  
Storage Period ◽  
Hplc Method ◽  
Initial Concentration ◽  
Ph Changes ◽  
Stability Indicating ◽  
Two Temperatures ◽  
The Mean ◽  
Glass Bottles ◽  
The Stability ◽  
Mean Concentration

OBJECTIVE: To determine the stability of spironolactone in an extemporaneously prepared suspension at 22 and 4°C over a three-month storage period. DESIGN: Spironolactone suspension (1 mg/mL) was prepared in syrup NF, carboxymethylcellulose, and purified water USP. The suspension was stored in ten amber glass prescription bottles; five were stored at 22°C and five at 4°C. Samples were drawn from each bottle and analyzed in duplicate (n=10) on days 0, 7, 14, 28, 42, 56, 70, and 91. Spironolactone concentrations were measured by a reproducible and stability-indicating HPLC method. Inspection of visual and pH changes also was performed on each study day. RESULTS: The mean concentration of spironolactone was always higher than 98 percent of its initial concentration. The pH and appearance of the suspension did not change substantially. CONCLUSIONS: Spironolactone was stable in a suspension containing syrup, carboxymethylcellulose, and purified water for three months during storage in amber glass bottles at both 22 and 4°C.

Stability of the Vertical Autorotation of a Single-Winged Samara

1992 ◽  
Vol 59 (4) ◽  
pp. 1000-1008 ◽  
Author(s):  
D. Seter ◽  
A. Rosen
Keyword(s):  
Equilibrium State ◽  
Equations Of Motion ◽  
Numerical Differentiation ◽  
Aerodynamic Stability ◽  
Small Perturbations ◽  
Stability Derivatives ◽  
Basic Equilibrium ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Derivatives Of

A numerical model to investigate the stability of the vertical autorotation of a singlewinged samara is presented. This model is obtained after the method of small perturbations about an equilibrium state is applied on the nonlinear equations of motion of the samara. The aerodynamic stability derivatives of the wing are obtained by numerical differentiation. The model is used in order to study the influence of different parameters on the stability. Since the stability is highly dependent on the basic equilibrium state, the influence of the different parameters on the basic state is also presented and discussed. The theoretical model is validated by comparing its results with qualitative experimental results.

An Application of Mixture Theory to Particulate Sedimentation

1980 ◽  
Vol 47 (2) ◽  
pp. 261-265 ◽  
Author(s):  
C. D. Hill ◽  
A. Bedford ◽  
D. S. Drumheller
Keyword(s):  
Particle Concentration ◽  
Equations Of Motion ◽  
Mixture Theory ◽  
Solid Particles ◽  
Two Phase ◽  
Small Perturbations ◽  
One Dimensional ◽  
Blood Sedimentation ◽  
The One ◽  
Extended Variational Principle

Equations for two-phase flow are used to analyze the one-dimensional sedimentation of solid particles in a stationary container of liquid. A derivation of the equations of motion is presented which is based upon Hamilton’s extended variational principle. The resulting equations contain diffusivity terms, which are linear in the gradient of the particle concentration. It is shown that the solution of the equations for steady sedimentation is stable under small perturbations. Finally, finite-difference solutions of the equations are compared to the data of Whelan, Huang, and Copley for blood sedimentation.

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